On Modeling the Mechanical Behavior of Matter: The Continuum Assumption

John C Criscione

Abstract

This paper is dedicated to Dr. Rajagopal, a great scientist, mathematician, and mentor. His excellence in theoretical analysis is at the highest level; yet when combined with his insight into the mechanics of real materials, I think Raj’s contributions are destined to be classics. Given my interest in the mechanics of soft tissues and the obvious challenges associated with anisotropic, inelastic, and non-linear behavior; Raj’s input, advice, criticism, and encouragement have been invaluable. I can think of no better tribute to Raj than to question our foundational principles and advance the boundary of their application. Moreover, the focus of this work is on the “raw material” of mechanics; the stuff that exists, has mass, and occupies space. The fact of the matter is matter, and how to model its mechanical behavior. Toward this end, we searched for a framework that is tautologically intact for discontinuous materials, and surprisingly, we found continuum mechanics.